Problem: $A$ $B$ $C$ If: $ AC = 55$, $ BC = 3x + 3$, and $ AB = 8x + 8$, Find $BC$.
Answer: From the diagram, we can see that the total length of ${AC}$ is the sum of ${AB}$ and ${BC}$ $ {AB} + {BC} = {AC}$ Substitute in the expressions that were given for each length: $ {8x + 8} + {3x + 3} = {55}$ Combine like terms: $ 11x + 11 = {55}$ Subtract $11$ from both sides: $ 11x = 44$ Divide both sides by $11$ to find $x$ $ x = 4$ Substitute $4$ for $x$ in the expression that was given for $BC$ $ BC = 3({4}) + 3$ Simplify: $ {BC = 12 + 3}$ Simplify to find ${BC}$ : $ {BC = 15}$